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We determine the expected error by smoothing the data locally. Then weoptimize the shape of the kernel smoother to minimize the error. Because theoptimal estimator depends on the unknown function, our scheme automaticallyadjusts to the unknown function. By self-consistently adjusting the kernelsmoother, the total estimator adapts to the data.  Goodness of fit estimators select a kernel halfwidth by minimizing a functionof the halfwidth which is based on the average square residual fit error:$ASR(h)$. A penalty term is included to adjust for using the same data toestimate the function and to evaluate the mean square error. Goodness of fitestimators are relatively simple to implement, but the minimum (of the goodnessof fit functional) tends to be sensitive to small perturbations. To remedy thissensitivity problem, we fit the mean square error %goodness of fit functionalto a two parameter model prior to determining the optimal halfwidth.  Plug-in derivative estimators estimate the second derivative of the unknownfunction in an initial step, and then substitute this estimate into theasymptotic formula.

Function Estimation Using Data Adaptive Kernel Estimation - How Much Smoothing?